Course Title : Engineering Mathematics B1

Code 20510
Course Year 2nd year
Class day & Period T1.T2:Wednesday・5,T3.T4:Friday・3,
Location kyotsu155
Credits 2
Restriction No Restriction
Lecture Form(s) Lecture
Language Japanese
Instructor T1.T2:E. Harada,T3.T4:J. Saitoh,

Course Description

The course introduces theory of complex functions and its applications.


Term-end examination and attendance.

Course Goals

To understand the properties of regular function. To learn Taylor expansion and Laurent expansion. To calculate residues. To learn some applications for engineering.

Course Topics

Theme Class number of times Description
Introduction 2 Definition of complex numbers, complex plane and review of vector analysis
Basic theory of complex functions 8 Derivative of complex functions.
Cauchy-Riemann equations.
Concept and properties of regular functions. Cauchy's integral theorem.
Cauchy's integral formula.
Taylor series and Laurent series.
Classification of singularities.
Residue theorem.
Various complex functions and their properties.
Application of theory of complex functions 4 Application of residue theorem to calculation of definite integrals.
Multivalued functions.
Learning achievement test 1 Learning achievement test.




Useful material is introduded during the lecture.


Basic Calculus (From the university curriculum: Calculus A and B, Advanced Calculus A).

Web Sites

Additional Information